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MODELING PARTICLE INJECTIONS–TEST PARTICLE SIMULATIONS
Xinlin Li
LASP, University of Colorado, Boulder, CO 80303-7814, USA
ABSTRACT
We model dispersionless injections of energetic particles
associated with magnetospheric substorms observed at
geosynchronous orbit and multiple discrete-energy ion
features and ‘nose’ signatures observed across a large
range of L and energy in the inner magnetosphere. Modeling these particle features enables us to probe more detailed effects of field configuration changes on particle
flux variations and to show how deeply into the magnetosphere impulsive electric and magnetic fields associated
with magnetic substorms can penetrate.
Key words: substorm, particle injection, dispersionless,
test-particle simulation, ‘nose’ event.
1. INTRODUCTION
In the Earth’s magnetotail, a dynamic region of the magnetosphere, abrupt magnetic field changes result in the
acceleration of energetic particles. If we were able to understand the development of magnetic and electric fields,
we would understand better the fundamental acceleration
process. However, the presently available measurements
show only local changes of the magnetic fields and sometimes of the electric fields. Although MHD or two-fluid
simulations provide an overall picture of the magnetic
field configuration of the magnetotail, these fluid models do not directly address energetic particle dynamics.
Another way to understand the field variations is to study
particle motion. Since changes in particle fluxes depend
on the magnetic and electric fields over a large region of
space, by studying the effects of various magnetic and
electric fields on the observed particles, we can learn to
interpret what the particle properties imply about global
conditions.
Energetic particle (10s–100s keV) injections into the inner magnetosphere are a common feature of magnetospheric substorms. Thus, energetic particle acceleration
and subsequent transport represents a key component of
understanding magnetospheric dynamics.
I first discuss a series of observations of energetic particle
injection associated with substorms and the importance
of test-particle simulations in understanding the substorm
injections. I will then describe the model, and finally,
show some examples of recent test-particle simulation
results with a focus on the ‘nose’ signature (Smith and
Hoffman, 1974).
2. OBSERVATIONS AND DISCUSSIONS
One of the characteristic features of substorm onset is
“dispersionless” particle injection, meaning that particles
with different energies enhance at the same time. Dispersionless injections are usually accompanied by rapid
changes of the magnetic field as the nightside magnetospheric field becomes more like a dipole field. This
“dipolarization” is one of the central features of substorms.
Measurements from satellites at geosynchronous orbit
separated only by a few hours around local midnight
show that dispersonless injections occur in a narrow region in longitude. Typically, satellites to the east of midnight only measure dispersionless injection of electrons
while satellites to the west of midnight only measure
dispersionless injection of protons (Reeves et al., 1991).
This is consistent with the fact that dipolarization occurs
within a limited local time sector, i.e., within the substorm current wedge (McPherron et al., 1973).
Measurements from satellites located near the same local
time but at different radial distances show that injections
occur first at larger radial distances (Reeves et al., 1996),
indicating that the injected particles come from outside
and propagate inward.
Figure 1 shows an example of measurements from three
geosynchronous satellites at different local times. The
electron injection was first detected by satellite 1, which
is dispersionless. As the electrons drift eastward, they
show more (satellite 2) and more (satellite 3) dispersion, because more energetic electrons drift faster. These
same electrons continued to drift around the Earth and
were detected by the satellite again. Protons, which drift
in the opposite direction, were first measured by satellite 3 when some dispersion had already occurred, because satellite 3 is far from the injection region. Later
they were measured by satellite 2. No proton data are
available from satellite 1. This particular observation has
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Figure 2. (Fig. 1 of Li et al. (1998) Modeled electric
field, Eφ , and magnetic field, Bz , in the equatorial plane
at geosynchronous orbit at different locations.
Figure 1. Differential fluxes of electrons and protons from
LANL observations in the early Jan. 10, 1997.
been well reproduced by test-particle simulations (Li et
al., 1998, 1999) (Fig. 4 and 5).
Another interesting phenomenon associated with substorm particle injections is multiple discrete-energy peaks
in ion energy spectra recently measured by the (CAMMICE/MICS and TIMAS) ion composition sensors on
the POLAR satellite. These spectra are seen as multiple
bands in energy-time plots (Fennell et al., 1998; Peterson
et al., 1998). Such features have long been observed near
geosynchronous orbit (e.g., Mauk and Meng; Grande et
al., 1992). The most striking feature from the POLAR
data is that these multiple bands occur over a large range
of L (L=3–8) and energy (a few keV to hundreds of keV)
independent of the mass of the ions. These events are
more likely to be observed during quiet times following
substorm activity (Fennell et al., 1998). We (Li et al.,
2000) have interpreted some of the observed ion bands as
the result of a time-of-flight effect of the particle’s drift
around the Earth, based on test-particle simulations.
Test-particle simulation is a useful tool for studying energetic particles because these particles represent a small
fraction of the total plasma number density, and their
feedback on the fields is usually negligible. Furthermore,
energetic particle dynamics cannot be directly described
by fluid or MHD simulations, and realistic kinetic simulations such as particle-in-cell simulations are still not
viable for global applications, given the current power of
computers.
There are several ways of carrying out test-particle simulations. One is to trace particles in the fields generated
by MHD simulation. Progress has been made in this di-
rection. For example, Birn et al. [1997, 1998] traced
both protons and electrons in the dynamic field generated
from MHD simulation. Their test particle simulation reproduced major features of the initial rise of the particle
injection at geosynchronous orbit. However, their MHD
simulation is limited, stopping at 5RE in the nightside.
Another way is to construct field models based on observations and physical principals and then trace particles in
these constructed fields. It is then much simpler to vary
different parameters in the model to compare the modeling results with observations.
3. MODEL AND RESULTS
We (Li et al., 1998) have constructed a time-varying
field model to simulate substorm particle injections. The
time varying fields are associated with the dipolarization.
When dipolarization occurs, the z-component of magnetic field, Bz , at the equator increases. Faraday’s law
tells us that an inductive electric field in the azimuthal direction is produced. These time-varying fields propagate
toward the Earth.
Figure 2 shows the time-dependent fields in the equatorial plane at geosynchronous orbit. An increase of Bz is
followed by a decrease, the net result is an increase of
Bz after the pulse has passed. The fields are centered at
midnight. The magnitude decays away from midnight,
simulating a localized dipolarization. These fields propagate at a speed of 100 km/s. We implement these fields
into the guiding center equations and trace particles.
Figure 3 shows the trajectory of two 900 equatorial pitch
angle electrons. Before the arrival of the pulse field, the
electrons perform a gradient-B drift whose drift speed is
energy-dependent. When the pulse arrives, the electrons
encounter an oppositely-directed magnetic field gradient
that can reduce or even reverse the local magnetic field
gradient, such that the electrons can drift in the opposite direction (westward). Meanwhile, each electron also
moves radially inward because of E B drift, which is
energy-independent. As each electron moves closer to
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the Earth, the background magnetic field eventually begins to dominate and the electrons again drift eastward,
the normal direction. As soon as the wave fields are no
longer present, the electrons perform only a gradient-B
drift, but in a stronger magnetic field region (closer to the
Earth) The temporal reversal of magnetic field gradient is
a significant feature of this model, leading to the successful simulation.
hour using this model. The time scale for forming a clas-
Figure 4 shows test-particle simulations for electrons that
incorporate the instrument response and satellite motion.
The dispersionless feature, drift echo, double-peak feature, even the width and shape of the flux enhancements
are more or less reproduced. Figure 5 shows the simulation results for protons using the same field model but
differing initial particle distributions. Most of the injected
electrons and protons originated from beyond 11RE in the
simulations of Li et al. (1998, 1999).
The multiple discrete ion features in the inner magnetosphere (Fennell et al., 1998; Peterson et al., 1998) are, in
many aspects, simply a manifestation of substorm associated particle injections. This has been simulated and
discussed in detail by Li et al. (2000). Here I focus on
a related phenomenon in the inner magnetosphere known
as a ‘nose’ event. The following results are from the same
test-particle run with a field model identical to the one in
Li et al. (2000) and with the initial proton distribution (a
kappa distribution) of Li et al. (2000), except for the initial inner boundary. Another difference is the motion of
the virtual satellite in the simulation.
Figure 6 shows the results from a virtual satellite located
at dusk but moving inward from L=9.5 to L=3.5 with a
speed of 0.04 RE /min, four times faster than in Fig. 3 of
Li et al. (2000). Initial proton distribution has the inner
boundary at L=5 (compared to L=3.5 in Li et al. (2000)).
The line plot is from selected energy channels; lines correspond to the differential fluxes of particles at different
energies. Particles are injected from the midnight region;
the satellite first measured the injections at Time=30
min at L7.8. Particles drift around the Earth, while the
satellite continues to move inward at local dusk. More
energetic ions drift faster and come back to the satellite
again, their flux peaks are identified as drift echoes.
The lines sometimes overlap each other, indicating that
the higher energy particle flux can at times surpass the
lower energy particle flux. The energy spectrum plot of
the same simulation includes results from many other
channels, incorporated with the instrument response.
Figure 3. Trajectory of two electrons initially placed at
the equatorial plane with r0 = 12RE , W0 = 26 keV, and
φ0 = 120 (dotted) and r0 = 14RE , W0 = 25 keV, and φ0 =
135 (solid).
Figure 4. (Fig. 3 of (Li et al., 1998)) Differential fluxes
of electrons from LANL observations in the early Jan.
10, 1997 in the left column: number 1, 2, and 3 correspond to spacecraft 1990-095 (LT=UT-2:30), 1991-080
(LT=UT+4:42), and 1994-084 (LT=UT+6:54) respectively.
Figure 7 is a replot of the energy spectrum: color-coded
time for fluxes above certain threshold vs L, showing the
inner edge of injected protons.
Figure 8 shows the results from the field model with
the initial inner boundary of the proton distribution at
L=7 and the virtual satellite moving inward at a speed
of 0.05RE /min. The nose structure, as shown in Figure 9,
also suggests that protons (plasmasheet ions) initially located beyond L=7 can be injected inside L=5 within an
Figure 5. (Fig. 2 of Li et al. (1999)) Same as Figure 4 but
for protons
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Figure 6. Top panel is a line plot for selected energy channels as labeled. The bottom panel is an energy spectrum plot of
the same simulation but with many more energy channels. The virtual satellite moves from 9.5RE to 3.5RE at local dusk
at constant speed, Vsatellite = 0:04RE /min. The inner boundary of the initial proton distribution starts at 5RE .
Figure 7. A different way to plot Figure 6: color-coded time for fluxes above certain threshold vs L, showing the motion
of the inner edge of the injected protons.
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Figure 8. Same as Figure 6 except the virtual satellite moves at faster speed, Vsatellite = 0:05RE /min and the inner boundary
of the initial proton distribution starts at 7RE .
Figure 9. A different way to plot Figure 8: color-coded time for fluxes above certain threshold vs L, showing the motion
of the inner edge of the injected protons.
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sic ‘nose’ event (Smith and Hoffman, 1974) using only
the convection electric field was many hours (Ejiri et al.,
1980). Here I demonstrate that the ‘nose’ structure can
also be formed in less an hour during a quiet time following a substorm onset.
The differences between Figs. 6 and 8 and between
Figs. 7 and 9 are the inner boundaries of initial proton distribution and the moving speeds of the virtual satellites.
Even under the same field model and initial distribution,
satellites traversing the inner magnetosphere differently
will observe different ion features depending on the relative timing and location of the satellites with respect to
the particle injection.
During quiet times, according to the conventional convection electric field model, the electric field is shielded from
the inner magnetosphere (Maynard and Chen, 1975). The
existence of ion drift echoes even after only moderate
substorm activity and the ‘nose’ structure shows that localized time-varying electric and magnetic fields such as
are modeled here can and do penetrate deeply into the
inner magnetosphere.
ACKNOWLEDGMENTS
The author gratefully acknowledges M. Temerin, D.
N. Baker, G. D. Reeves, R. D. Belian, J. F. Fennell,
and W. Peterson for their contributions to the published
work (Li et al., 1998, 1999, 2000) and O. Lennartsson
for discussion about the TIMAS instrument, K. Trattner and A. Rakow for helping with the graphic display. This work was supported by NSF/ATM-9901085
and NASA/NAG5-9421.
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